From what i understand, the vast majority of Chareidi (Ultra-Orthodox) Jews do not give any significance to Yom HaAtzmaot (Israeli Independance Day) other than a minority who perhaps give thanks for the good that has come out of the founding of the State. My question is, would it be Mutar or even suggested to say “Chag Sameach” or some other form of holiday greeting to someone who is non-observant in order to be Mekarev him? What about someone who does give some religious significance to the day, what would be to greet him as such?
I am not aware of a halachic probem with such a greeting. Even if a person does not give any significance to the day, the greeting is merely a way of acknowledging that the person you are greeting does consider it a special day.